Abstract:

In this talk, we will try to illustrate the potential of stochastic calculus as a tool for proving inequalities with a geometric nature. We'll do so by focusing on the proofs of two new bounds related to the Gaussian Ornstein-Uhlenbeck convolution operator, which heavily rely on the use of Ito calculus. The first bound is a sharp robust estimate for the Gaussian noise stability inequality of C. Borell (which is, in turn, a generalization of the Gaussian isoperimetric inequality). The second bound concerns with the regularization of $L_1$ functions under the convolution operator, and provides an affirmative answer to a 1989 question of Talagrand. If time allows, we will also mention an application of these methods to concentration inequalities for log-concave measures. Based in part on a joint work with James Lee.

In this talk, we will try to illustrate the potential of stochastic calculus as a tool for proving inequalities with a geometric nature. We'll do so by focusing on the proofs of two new bounds related to the Gaussian Ornstein-Uhlenbeck convolution operator, which heavily rely on the use of Ito calculus. The first bound is a sharp robust estimate for the Gaussian noise stability inequality of C. Borell (which is, in turn, a generalization of the Gaussian isoperimetric inequality). The second bound concerns with the regularization of $L_1$ functions under the convolution operator, and provides an affirmative answer to a 1989 question of Talagrand. If time allows, we will also mention an application of these methods to concentration inequalities for log-concave measures. Based in part on a joint work with James Lee.

## Date:

Thu, 31/03/2016 - 14:30 to 15:30

## Location:

Manchester Building (Hall 2), Hebrew University Jerusalem